Geometric study of non-constant vector fields making hyperbolic space Ricci-Bourguignon solitons
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915554654158848 |
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| author | Diop, Mafal Ndiaye Bousso, Abdou Khoule, Cheikh Ndiaye, Ameth |
| author_facet | Diop, Mafal Ndiaye Bousso, Abdou Khoule, Cheikh Ndiaye, Ameth |
| contents | The objective of this paper is to deepen the study of vector fields on hyperbolic spaces $\mathbb{H}^n$ that transform them into a Ricci-Bourguignon soliton. Starting from a recent work in \cite{bousso2025ricci} which characterizes these fields as Killing fields of a specific shape, we propose a detailed geometric study of their structure and behavior in the dimensions $n=2, 3$ and $n\geq 3$. In odd dimension we show that the dual form of these vectors are contact forms. This work aims to enrich the understanding of self-similar solutions of the Ricci flow in a more general context. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_12745 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric study of non-constant vector fields making hyperbolic space Ricci-Bourguignon solitons Diop, Mafal Ndiaye Bousso, Abdou Khoule, Cheikh Ndiaye, Ameth Differential Geometry 37C35, 37D40 The objective of this paper is to deepen the study of vector fields on hyperbolic spaces $\mathbb{H}^n$ that transform them into a Ricci-Bourguignon soliton. Starting from a recent work in \cite{bousso2025ricci} which characterizes these fields as Killing fields of a specific shape, we propose a detailed geometric study of their structure and behavior in the dimensions $n=2, 3$ and $n\geq 3$. In odd dimension we show that the dual form of these vectors are contact forms. This work aims to enrich the understanding of self-similar solutions of the Ricci flow in a more general context. |
| title | Geometric study of non-constant vector fields making hyperbolic space Ricci-Bourguignon solitons |
| topic | Differential Geometry 37C35, 37D40 |
| url | https://arxiv.org/abs/2510.12745 |